Secured at both ends, a steel wire possesses a fundamental...

The fundamental frequency of the string is given as $f_{1} = 200 \text{ Hz}$.

The maximum audible frequency for the person is f_{\text\max} = 14 \text{ kHz} = 14000 \text{ Hz}.

The frequency of the $n^{\text{th}}$ harmonic of a string secured at both ends is given by $f_{n} = n f_{1}$.

For the sound to remain audible, the frequency of the harmonic must be less than or equal to the maximum audible frequency:

f_{n} \le f_{\text\max}

$n \times 200 \le 14000$

$n \le \dfrac{14000}{200}$

$n \le 70$

The highest harmonic that can be produced and still remain audible is $70$.